Statistical inferences will be studied for clinical trials in which a control and one or more treatment groups are compared. The investigation will greatly facilitate the use of interim analyses and the incorporation of apriori information about the ordering of the treatments into such inferences. Interim analyses have been proposed by several authors in clinical trials where subjects are followed for a long period of time. We propose to construct tables of decision constants for such clinical trials when there are two treatment arms and the applied investigator wishes to conduct one, two or three interim analyses. Guidelines will also be presented to help an investigators select an appropriate spending function for alpha. For both one-sided and two-sided alternatives, the decision constants will be obtained by solving simultaneous systems of nonlinear equations. In some clinical trials, the ordering of the treatments is believed to be known, or at least it is believed that the treatments are as effective (or harmful) as the control. It is well documented that utilizing ordering information typically increases the efficiency of a statistical procedure and thus such procedures will be investigated. The procedures considered allow for censored data and make use of covariate information. In the studies of interest, the patients are followed for a period of time to determine if a certain condition occurs and the inferences will be based on either the times of occurrences or the time intervals in which the event occurs. Preliminary studies indicate that an order restricted log-rank test performs well in a proportional hazard setting. The power function of the ordered log-rank test will be compared with those of its competitors for alternatives that have proportional hazards and for alternatives that do not. Guidelines will be developed for the use of these tests. Approximations for the power function of the ordered log-rank test will be developed so that experiments with a desired power can be designed. The inferences for ordered Cox regression which are available will be generalized to allow for covariates and other order restrictions. Furthermore, a comprehensive computer package for conducting inferences based on ordered Cox regression will be developed.